Solve -16r^2-2=0

$$- 16 r ^ { 2 } - 2 = 0$$

Solve for r

$$r=-\frac{\sqrt{2}i}{4}\approx -0-0.353553391i$$

$$r=\frac{\sqrt{2}i}{4}\approx 0.353553391i$$

Steps by Finding Square Root

Add 2 to both sides. Anything plus zero gives itself.

$$-16r^{2}=2$$

Divide both sides by -16.

$$r^{2}=\frac{2}{-16}$$

Reduce the fraction \frac{2}{-16} to lowest terms by extracting and canceling out 2.

$$r^{2}=-\frac{1}{8}$$

The equation is now solved.

$$r=\frac{\sqrt{2}i}{4} r=-\frac{\sqrt{2}i}{4}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-16r^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-16\right)\left(-2\right)}}{2\left(-16\right)}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-16\right)\left(-2\right)}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$r=\frac{0±\sqrt{64\left(-2\right)}}{2\left(-16\right)}$$

Multiply 64 times -2.

$$r=\frac{0±\sqrt{-128}}{2\left(-16\right)}$$

Take the square root of -128.

$$r=\frac{0±8\sqrt{2}i}{2\left(-16\right)}$$

Multiply 2 times -16.

$$r=\frac{0±8\sqrt{2}i}{-32}$$

Now solve the equation r=\frac{0±8\sqrt{2}i}{-32} when ± is plus.

$$r=-\frac{\sqrt{2}i}{4}$$

Now solve the equation r=\frac{0±8\sqrt{2}i}{-32} when ± is minus.

$$r=\frac{\sqrt{2}i}{4}$$

The equation is now solved.

$$r=-\frac{\sqrt{2}i}{4} r=\frac{\sqrt{2}i}{4}$$